Find the angle that the vector R

[NINHARDCOREFAN]

part 1 of 2
Two vectors A and B, are lying in the xy
plane and given by
A = Axi +Ayj
B = Bxi +Byj
(x y are subscripts)

where A x = 4.4 m, A y = 1.74 m, B x = 7.58 m, B y = -6.76 m. Let R = A+B.
Find the magnitude of R. Answer in units
of m.

So it is
A = 4.4mI + 1.74mJ
B = 7.58mI - 5.02J

I have found out R by using the distance formula
sqrt(11.98^2 + 5.02^2) = 12.9893 m(which is right)

part 2 of 2
Find the angle that the vector R makes from
the positive x axis. Choose your answer to be
between -180 # and +180 # . The positive an_
gular direction is counter clockwise measured
from the x axis. Answer in units of # .

I tried this problem using the cosine law.
-5.02squared-11.98squared-12.99squared
______________________________________(division)
-2*11.98*12.99

I got 22.73 degrees. But when I sumbit this answer, it says I'm wrong. Can you figure out what I'm doing wrong?

 

[HallsofIvy]

The angle you are looking for, the angle the vector R makes with the x-axis is NOT an angle in the triangle formed by the three vectors. Also, you have the cosine law wrong (it may be a typo).
It is a^2= b^2+ c^2- 2bc cos(A) so cos(A)= (a^2- b^2- c^2)/(2bc).

In any case, the simplest way to do this is to look at the vector
R only. You know the components of R. Look at the right triangle formed by the vector and it's components and think "tangent"!

 

[enigma]

Originally posted by NINHARDCOREFAN
where A x = 4.4 m, A y = 1.74 m, B x = 7.58 m, B y = -6.76 m. Let R = A+B.
Find the magnitude of R. Answer in units
of m.

So it is
A = 4.4mI + 1.74mJ
B = 7.58mI -5.02J

B_y is incorrect (it's the y-comp of R), but it looks like you caught that in the next part.

I have found out R by using the distance formula
sqrt(11.98^2 + 5.02^2) = 12.9893 m(which is right)

part 2 of 2
Find the angle that the vector R makes from
the positive x axis. Choose your answer to be
between -180 # and +180 # . The positive an_
gular direction is counter clockwise measured
from the x axis. Answer in units of # .

I tried this problem using the cosine law.
-5.02squared-11.98squared-12.99squared
______________________________________(division)
-2*11.98*12.99

I got 22.73 degrees. But when I sumbit this answer, it says I'm wrong. Can you figure out what I'm doing wrong? [/B]

Just find the arctan. rise/run = tan θ , so atan (rise/run) = θ

Be sure you know what quadrant you're in. atan is only defined for +- 90 degrees, so you will need to add 180 degrees if you're in the second or third quadrants.

 

[NINHARDCOREFAN]

After I did that I got 22.74, the same answer as I did before, which is wrong.

 

[NINHARDCOREFAN]

The answer was -22.74(QIV), which is same as 22.74(QI)

 

[HallsofIvy]

Why is "-22.74(QIV)" the same as "22.74(QI)"? They look very different to me!

 

[NINHARDCOREFAN]

I figured that out last night, I thought the problem said that answer has to be between 0 and 180 but then realized that it was between -180 and 180.